# Statistics - Inverse Gamma Distribution

Inverse Gamma Distribution is a reciprocal of gamma probability density function with positive shape parameters ${\alpha, \beta }$ and location parameter ${ \mu }$. ${\alpha }$ controls the height. Higher the ${\alpha }$, taller is the probability density function (PDF). ${\beta }$ controls the speed. It is defined by following formula.

## Formula

${ f(x) = \frac{x^{-(\alpha+1)}e^{\frac{-1}{\beta x}}}{ \Gamma(\alpha) \beta^\alpha} \\[7pt] \, where x \gt 0 }$

Where −

• ${\alpha}$ = positive shape parameter.

• ${\beta}$ = positive shape parameter.

• ${x}$ = random variable.

Following diagram shows the probability density function with different parameter combinations.

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